Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-7y &= 9 \\ 6x+9y &= -9\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $9y = -6x-9$ Divide both sides by $9$ to isolate $y$ $y = {-\dfrac{2}{3}x - 1}$ Substitute this expression for $y$ in the first equation. $-5x-7({-\dfrac{2}{3}x - 1}) = 9$ $-5x + \dfrac{14}{3}x + 7 = 9$ Simplify by combining terms, then solve for $x$ $-\dfrac{1}{3}x + 7 = 9$ $-\dfrac{1}{3}x = 2$ $x = -6$ Substitute $-6$ for $x$ back into the top equation. $-5( -6)-7y = 9$ $30-7y = 9$ $-7y = -21$ $y = 3$ The solution is $\enspace x = -6, \enspace y = 3$.